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Properties

Label 806.2.bw
Level $806$
Weight $2$
Character orbit 806.bw
Rep. character $\chi_{806}(51,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $288$
Newform subspaces $1$
Sturm bound $224$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 806 = 2 \cdot 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 806.bw (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 403 \)
Character field: \(\Q(\zeta_{30})\)
Newform subspaces: \( 1 \)
Sturm bound: \(224\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(806, [\chi])\).

Total New Old
Modular forms 928 288 640
Cusp forms 864 288 576
Eisenstein series 64 0 64

Trace form

\( 288 q + 72 q^{4} + 32 q^{9} + O(q^{10}) \) \( 288 q + 72 q^{4} + 32 q^{9} - 10 q^{13} - 12 q^{14} - 72 q^{16} + 10 q^{17} - 6 q^{22} - 48 q^{23} + 104 q^{25} + 12 q^{26} - 18 q^{27} + 36 q^{29} + 64 q^{30} - 28 q^{35} + 128 q^{36} - 70 q^{38} + 12 q^{39} - 6 q^{42} - 56 q^{43} - 58 q^{49} - 26 q^{51} + 10 q^{52} - 6 q^{53} + 72 q^{55} + 2 q^{56} - 140 q^{61} + 16 q^{62} + 72 q^{64} - 4 q^{65} + 40 q^{68} + 96 q^{69} - 28 q^{74} - 166 q^{75} - 68 q^{77} + 60 q^{78} - 80 q^{79} - 76 q^{81} + 24 q^{87} - 14 q^{88} + 114 q^{90} - 12 q^{91} + 8 q^{92} - 24 q^{94} + 100 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(806, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
806.2.bw.a 806.bw 403.az $288$ $6.436$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{30}]$

Decomposition of \(S_{2}^{\mathrm{old}}(806, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(806, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(403, [\chi])\)\(^{\oplus 2}\)